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Factorization of Summability‐Preserving Generalized Limits
Author(s) -
Raimi Ralph A.
Publication year - 1980
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-22.3.398
Subject(s) - mathematics , limit (mathematics) , factorization , banach space , bounded function , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , algorithm
On the space of bounded sequences, let U (the Césaro operator) be defined by Uf ( n ) =1 n ∑ k = 1 n f ( k ) . Then if l is any generalized limit, l O U is a Banach limit which also extends Césaro summability. An example is given to show that not every Banach limit extending Césaro summability is factorizable in this way.